3/8x=4/5x+10

Solution for 3/8x=4/5x+10 equation:

3/8x=4/5x+10

We move all terms to the left:

3/8x-(4/5x+10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

3/8x-4/5x-10=0

We calculate fractions


15x/40x^2+(-32x)/40x^2-10=0

We multiply all the terms by the denominator


15x+(-32x)-10*40x^2=0

Wy multiply elements

-400x^2+15x+(-32x)=0

We get rid of parentheses

-400x^2+15x-32x=0

We add all the numbers together, and all the variables

-400x^2-17x=0

a = -400; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-400)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-400}=\frac{0}{-800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-400}=\frac{34}{-800}
=-17/400
$